Piezoelectric device and method of manufacture



June 24, 1947. M H 2,423,061

PIEZOELECTRIC DEVICE AND METHOD OF MANUFACTURE Filed April 29, 1944 Z (OPT/CAL) Z Y (/WECHAN/CAL) ATTORNEY Patented June 24, 1947 PIEZOELECTRIC DEVICE AND METHOD OF MANUFACTURE Henry M. Bach, Lawrence, N. Y., assignor to Premier Crystal Laboratories, Inc., New York, N. Y., a corporation of New York Application April 29, 1944, Serial No. 533,317

4 Claims. (Cl. 171327) This invention relates to piezo-eiectric devices and more particularly to piezo-electric crystals which are primarily intended for use in relatively low frequency systems. i

A principal object of the invention is to provide an improved piezo crystal for use in systems of the order of 650 kc. or less, and which have substantially zero temperature coeiilcient of frequency and are substantially free from spurious vibrations.

Another object is to provide an improved thickness shear mode crystal which is of the so-cailed general AT cut and wherein the face shear vibrations are at least 25% removed in frequency from the thickness shear vibrations.

Another object is to provide a method of dimensioning AT cut crystals by proportioning the X, Y and Z dimensions so as to utilize mainly the thickness shear mode of vibration without undesirable coupling to the face shear mode of vibration.

Another object is to provide a method of dimensioning a thickness shear mode type of crystal so that the crystal can be cut according to general AT procedure but with considerable latitude, enabling the method to be used for mass production of relatively low frequency crystals e. g., those of the order of 650 kc. or less.

A further feature relates to a piezo-electric frequency control crystal requiring a small amount of quartz while possessing optimum starting characteristics and activity.

Another feature relates to a piezo crystal for use in holders of the adjustable air-gap type enabling a wide range of air-gap adjustments to be made without changing the activity or starting characteristics.

Another feature relates to an improved AT cut crystal wherein the mechanical coupling between the face shear mode of vibration and the thickness shear mode of vibration is substantially zero, and wherein frequency variations in the applied Ey' field can be varied at least plus or minus 25% with respect to the X shear frequency without producing any spurious responses.

Other features and advantages not particularly set forth will be apparent after a consideration of the following detailed descriptions and the appended claims. In the drawing the single figure shows one type of quartz plate having an orientation in accordance with the invention.

In the past few years there has been an ever increasing demand for crystal oscillator plates in the frequency range below 600 kc., particularly from 150 kc. to 500 kc. for use in instrument landing systems, simultaneous radio range and range beacons for aircraft, as well as for use in frequency modulation transmitters employing the Armstrong system. These plates are required to operate over wide variations in ambient temperature, with negligible frequency and activity change. The plates are required to have excellent starting characteristics and to be free from spurious response. These plates are mounted in variable air-gap types of holders in order to adjust individual units to zero beat when changed from one transmitter to another.

Originally in manufacturing these plates, X or Y cuts were employed but these plates had to be discarded because of their high temperature coefficient, presence of spurious response, and in ability to operate uniformly as a function of airgap adjustment. With the X cut crystal wherein the electric field is developed by electrodes perpendicular to an X axis direction, there are possible three extensional modes, one associated with each dimension of the plate Xx, Yy, and Z. In addition to these extensions the YZ or face shear ,type of vibration likewise is present. The YZ shear is strongly coupled to flexural vibrations, and it will be appreciated that with these possible modes of vibration and their harmonics, the secondary spectrum of the X plate left much to be desired. The Y cut possessed an extremely high temperature coeflicient and was strongly coupled mechanically to the XZ face shears, as well as XZ fiexures and KY flexures. Even with carefully dimensioned plates it was extremely difficult to manufacture Y-cut plates in mass production that would be free from activity dips over an extended temperature range.

Koga in 1933, as well as Lack, Williard, and Fair, Bokovoy and Baldwin and others, developed high frequency low drift oscillator plates known as the AT, or V-cut. This new out had a greatly simplified secondary spectrum and had a zero frequency temperature coeflicient. This plate which is in effect a Y-cut rotated substantially +35 15' about an X axis so that it is substantially 2 58' oil parallelism with a minor rhomb face, basically is a thickness shear type of oscillator (XY' shear) The magnitude of the troublesome mechanical coupling between the XY shear and the ZX shear in the Y cut is governed by the value of the Cu elastic constant which reduces to zero at +31". Hence at the AT orientation the value of the C56 elastic constant is low making the mechanical or elastic coupling between the AT or XY shear and the face shear (Z'X) low. However, when the AT" plate was tried in (Z'X) type. The main reasons for the troubles with the low frequency AT plates were due to activity hops with accompanying frequency discontinuities when the temperature of the plates were varied. These hops may be traced to a secondary frequency spectrum which alters the desired vibrations at certain temperatures, or over portions of the temperature range. This secondary frequency spectrum renders the desired vibrations a complex resultant of shears and ilexure vibrations and usually will raise or lower the frequency of the desired vibration from its calculated value considering it a simple XY' shear. The vibrations making up the secondary spectrum will have high temperature coefficients (usually negative) and hence their influence on the desired vibration will vary widely with temperature, thus causing the desired vibration to behave discontinuously as a function of temperature. v

Koga had first disclosed zero coemcient face shear frequency oscillator plates, and these plates were further developed e. g., CT, DT, ET, and FT, etc. The advantage of these low frequency face shear plates over the known low frequency AT" or thickness shear was that the frequency determining dimensions i. e., the length (X) and the width (Z) were much larger than the third dimension, th thickness (Y'), and the secondary spectrum of the plates was greatly simplified. The only troublesome secondary responses were flexures which could be removed from the desired face shear frequency by altering the thickness or Y dimension which would vary the frequency of the fiexure without changing the face shear frequency appreciably.

However, there are several disadvantages to the face shear plate. The face shear is closely coupled to fiexures in the plate which give rise to substantial acoustic radiation. The face shear is a rather weak oscillator, and its activity is greatly a, function of its mounting. The acoustic radiation limits its usefulness in variable air-gap holders, and its type of vibration requires elaborate retainer ring construction to prohibit lateral motion without impairing activity, for if there. is any restraint placed at points on the periphery than at substantially nodal regions, the vibrations are greatly reduced in amplitude, or are damped completely. Due to the requirements of flatness on the base electrode as well as on the major surfaces of the plate, the plate has a tendency to stick to the base electrode, which dampens the face shear oscillations of the plate. Further, if the plate becomes even slightly wedged in the retainer, the plate will stop oscillating due to a reduction of its Q to a lower value than will permit sustained oscillation in the oscillator. The face shear will exhibit a zero temperature coefllcient of frequency at but one temperature and the frequency will change parabolically about the zero frequency-temperature point. Thus when the plate is required to operate over a wide temperature range the temperature coefficient, the rate of change of frequency with temperature, at the extremities of the range is substantial, being of the order of approximately 7.5 parts per million per degree centigrade for the CT crystal at the extremities of a 60 C. to +90 C. temperature range. This square law frequency temperature relationship was substantially eliminated by the GT cut crystal which in effect is a face shear orientated plate which is then rotated 45 about its Y or thickness dimension. This reduces the face shear to its two components, an extension-compression mode along the length accompanied by a compression-extension along the width. By making the plate rectangular the modes along the width and length are separated in frequency and by using the mode along the one dimension, the temperature coeillcient of the vibration may be altered by vary ing length of the other dimension (varying the frequency of the coupled mode). The temperature frequency curve of the GT, when properly adjusted, is a. cubic, and the portion of substantially zero slope exists over a wide temperature range (approximately (3.). However, the inherent presence of the second frequency well within 25% of the desired frequency renders the GT useless for low frequency military and aircraft service wherein specification requirements demand no spurious response within :25% of desired frequency.

Referring to the drawing, it will be seen that the cut of plate contemplated by the invention is of the well-known AT type being oriented about the Z or optical axis at an angle of 34 50 in a direction of parallelism with a minor rhomb face of the mother crystal. The rectangular parallelepiped forming the cut, contains the X direction as two of its four bounding or peripheral edges. Hence the major surfaces of the plate are 2)! planes which are rotated about the X axis so they cut the ZY plane at an angle of .34 50' with respect to the normal ZX plane.

The thickness of the plate will be referred to hereinafter as the Y, the length will be referred to as the X and the width as the Z. The electric field will be impressed across the Y and will have a component Ey, in the Y direction of Eyf. The electric field in the X direction will be equal to zero (Ex=0) since the crystal blank is always oriented closer than 15' of the X axis. Accordingly therefore, we will expect that this Ey' component will excite XY' shear vibrations, Z'X shear vibrations as well as flexural vibrations KY and Z)! and which are mechanically coupled to th shears. Since Ex=0 we will find that the Xx, Yy and Z, extensional vibrations and the YZ shear willnot be excited, either electrically or mechanically due to coupling.

In any system we can denote a stress-strain deformation by a tensor which will have nine component vectors:

Xx; Yy; 2:; xy; Yz; Xz; Yx; Zy; Zx However, in the crystal plate we never have a net rotation about X, Y, or Z axis i e., the work done integrated over any number of periods of vibration always=0; no K. E. is lost and no P. E. is gained. For u+n a couple would exist that would cause rotation, and a gain or loss of energy to the system. Hence due to conservation of energy m=n or our tensor reduces to six components Xx; Yy; Zz; X Yz; Xz, three extensions of the form car and three shears of the form 411;.

Because of the symmetry about the Z axis, and the symmetry in the XY plane it may be readily shown that:

Ex can cause Xx; Yy} Z2; Yz Ey can cause Xy; Xz

Now the AT orientation is at an angle wherein themechanical (or elastic) coupling between the face shear (Xz') and the thickness shear (Xy') is nearly zero. However, it is required that for frequency of E. varied 125% from frequency of the Xv shear there shall be no spurious response from the plate. Accordinll it is necessary to dimension the plate so that the In or face shears are at least 25% removed from the frequency ofthe Xy' shear. Hence with the impressed Ey', we will generate:

X, shear (thickness shear) x. shear (face shear) x, iiexure v x. flexures (coupled closely to X. shear harmonics of above) We note that since Er=0 the three extensions and the Z'y' shear cannot be excited by the Eu field.

Now the frequency of the Xv shear is a function of the X and the Y dimensions, that is:

wherein F denotes shear vibration frequencies and F denotes ilexural vibration frequencies.

F varies inversely with change in either dimension whereas F varies inversely with change in longer dimension and directly with change in shorter dimension.

Since the x, Y and Z dimensions are commensurable in the low frequency AT plate, it is found that careful dimensioning of the plate must be followed if y the XY shear vibration is to provide aplate having the aforementioned prerequisites. This invention deals with dimensioned AT plates for the frequency range below 600 kc.

The XY' shear frequency is a function of the X and the Y dimension, hence by varying X, Y and Z, we will obtain a plate vibrating in X, shear wherein coupling to other modes is removed at least 25%.

The frequency of the Xy' shear is represented y which for the case in question reduce to:

For the low frequency crystals X and Y will be commensurable and higher order values for m and n will yield frequencies of vibration substantially removed from the desired frequency. In the above, frequency is expressed in kilocycles; Y is in millimeters; X i in millimeters; and K shear is a constant, a function of the shear elastic constant for the particular orientation, and the density of quartz. When X Y' (as in high frequency plates) this reduces to Kshm/Y'. In the low frequency plate it can be seen that the X dimension plays an important part in determining the thickness-shear frequency of the plate.

The frequency of the first XY ilexure will be determined approximately by the formula The frequency of the second, third, fourth flexures may be obtained by multiplying the frequency obtained from (3) a factor [('n-+-.5)/1r] where n=2, 3, 4, etc. A consideration of the type of motion of the XY' shear and iiexure shows that the odd shear (AT) will be mechanically 6 coupled to even order ilexures (n of form 2.7 where J=l,2. N) when used in the variable air-gap type of crystal holder.

The second Z fiexure coupled to the face shear vibration may be given by F'izs'=620/G wherein a=::=z' for a square plate, and

wherein m and n are integers and the values ofx and Z must be again chosen to insure that the face shear frequency for m=l, n=l, and for m=2, n=2, etc. for a substantially square plate (X #Z') are as far as possible removed from the desired XY' shear frequency.

Since we are.c0nsidering nearly square plates the face shear frequency of vibration may be given by:

for a nearly square plate. From Equations 4 and 6, we see that the length and width dimensions of the plate according to the invention produce a thickness-shear frequency which should lie midway between F11 and Fan or F r-54650; or above 6200/11 by 25% (7) By following ('7) the plate will be free from Xv,

face shear and from Z: fiexure.

Thfl ratio X/Y' and Z'/Y =Rxy', and Rs'y' 1S then determined to obtain freedom from X," and Z, flexure modes. Combining Equations 2 and 7:

Equation 9 denotes optimum ratio Bay for Xy' shear with maximum freedom from face shears.

The Xy' odd shear cannot couple to an odd flexural mode-it will couple to even flexural modes only. This is evident since in odd flexures the ends are out of phase and in even flexures the ends are in phase, wherea in odd shears the ends are in phase. Using the same type of analysis as given above on the face shears, it is found that the Xy' shear as above determined, is of the form M =N= l (see Equation 2). hence the dimension ratio 2.614 should be ideal since it is midway between the second and fourth flexural in the Xy' direction.

Therefore in its preferred form, the crystal is square at Rw=Rvw=-2.6 and if desired, the Re, may be reduced to .5 if necessary.

Considerable work, both theoretical and experimental over the past year and one-half has been done to obtain optimum values for the X, Y and Z dimensions for these plates. termined that nosingle set of ratios will be possible for these optimum values over the entire frequency range, due to the requirement that the plate shall never be larger in major dimensions a certain'amount e. g., approximately 30 mm. square. Whenever the ratio X/Y=R1w or X'/Y"=Rm are changed, the angle of cut for a zero temperature coefficient will likewise change discontinuously. This is due to the presence of coupled vibrations wherein the resultant vibration may be either positive or negative in temperature coefllcient depending on the predominance of one or more of the shears or flexures. Thus it is necessary to change the orientation of the plate to give the XY shear modulus a posi- I tive or negative coefflcient in order that the resultant vibration may be zero. It has been shown by Koga as well as Lack, Willard and Fair, that the temperature coefficient of the XY' shear modulus goes through zero at approximately +35 Below 35 15' the temperature coefllcient of the shear modulus is positive and above 35 15 the modulus is negative.

Production requirements are that but one angle of out be used for all of the low frequency plates. This will permit plates to be most economically diced from wafers, will permit the use of one orientation angle Jig, and will permit the complete salvage of plates inadvertently ground too small for a particular frequency.

Accordingly therefore, the ratios Rxy' and Rs'y' and the proper value of Y as a function of frequency have been obtained according to the above method of proportioning dimensions to provide a finished low frequency plate with zero temperature coefficient and with but a single 2': orientation angle.

It should be pointed out that although the mechanical coupling between the XY shear and the Z)! shear inherently is low for the +35 orientation, the oscillator circuits in which these plates are used are, for the most part, designed to operate equally well over a wide frequency range without tuning. Therefore, the Ey' field may excite the Z)! shear electrically rather than the XY' shear unless the Z)! shear frequency is far removed from the desired XY' shear frequency. A few oscillators are of the tuned plate type, and inexperienced operating personnel may inadvertently tune the oscillator to a Z)! shear mode rather than to the XY shear unless the Z)! shears are suitably far removed from the desired XY' shear frequency as above described.

For the frequency range 150 ire-600 kc. the dimensions of the finished plate are, according to the invention, given by the following formulae which have been calculated by applicant from the above considerations, and have been tried in practice.

(a) Freq. range 150-300 kc.:

It has been de- These dimensions provide an oscillator plate of optimum starting characteristics, zero temperature coemcient and complete freedom from spurious response within at least :25% of the desired frequency.

The temperature frequency relationship of these plates is much flatter than the relationship for the face shear type of plate. The frequency change with temperature is substantially linear rather than following the square law characteristic of the face shears. The coemcient may be altered by changing the dimensional ratios. For example, decreasing the ratio Ri'w=Z'/Y' will make the coefficient more negative and increasing the ratio Rs'y' will render coemcient more positive. Since small changes in the Z dimension will not have much effect on the XY' shear frequency the coefficient may be adjusted exactly to zero by changing the ratio Ra'y'. However, if the orientation angle Zx is maintained within :15 the coefilcient will always be well below 1 cycle per mo. per degree 0.

The orientation angle X='that is the rotation about the Z axis of the plate that will render the X axis direction out of the plane of the major surface should be equal to 0:15'. If this angle is allowed to deviate more than the limit stated. trouble is experienced with these dimensional blanks due mostly to the fact that the Ex field will not equal zero and the secondary spectrum may become more complex. The rotation angle X 'the rotation of the blank, about the Y axis rendering the X axis direction out of the edge or minor surfaces also shouldbe held to 0:15'. The face shear vibration will be broken up into extension components if the Xy' angle is permitted to deviate from 0 and the secondary spectrum of the plates will b greatly altered. It has been found that :15 may be readily maintained in production.

It should not be construed that a deviation of :30 or even i1 for the Xv or X, angles will render these plates useless. However it is found that the plates may have to be hand-tailored" or at least all will not be uniform unless the :15 angle tolerance is maintained.

Making oscillator plates according to the above formulae will provide in all cases, plates that will have no activity dips over a temperature range of at least 60 D, to C. and will be completely free from spurious response for at least 25% above and below the desired frequency.

One of the great advantages of a crystal cut as above described is that it is capable of use in a wide variety of oscillator circuits. Heretofore it has been usually necessary to restrict a given crystal one generic type of oscillator circuit. The crystal according to the invention is also capable of use in circuits where one of the crystal electrodes is directly grounded.

" What I claim is:

1. The method of manufacturing piezo crystals for utilization mainly of the thickness shear mode of vibration which comprises cutting a crystal plate so that its surface of greatest area lies substantially parallel to the "X axis of the mother crystal and inclined at an angle of between 33 and 36 with relation to the optical axis of the mother crystal as measured in a plane perpendicular to said surface, the X and Y' crystal di mensions being proportioned in the ratio of approximately 2.6 to 1, where X is the dimension along the electric axis, and Y is the dimension along the axis perpendicular to said surface.

2. The method of manufacturing piezo crystals for utilization mainly of the thickness shear mode of vibration which comprises cutting a crystal plate so that its surface of greatest area lies substantially parallel to the "X axis of the mother crystal and inclined at an angle of between 33 and 36 with relation to the optical axis of the mother crystal as measured in a plane p rpendicular to said surface, the plate dimensions being proportioned so that the said surface is approximately square with the ratio X/Y'=2.6 and so that the ratio Z'/Y is approximately 2.6, X being the dimension along the X axis, Z being the dimension along the rotated Z axis, and Y being the dimension along the axis perpendicular to said surface.

3. A thickness-shear mode piezo crystal for relatively low frequency operating circuits comprising a substantially AT cut crystal in which the Y dimension is of the order of 4 to 10 mm. and the X and Z' dimensions are approximately equal, the ratio of the x dimension to the Y dimension being approximately 2.6 to l.

4. The method of predetermining a desired fundamental thickness-shear mode of vibration of a quartz crystal which is substantially free from REFERENCES CITED The following references are of record in the file of this patent:

UN'I'IED STATES PATENTS Name Bokovoy Bokovoy Lack et al OTHER REFERENCES Proceedings Institute of Radio Engineers, May 1937, page 561. (Copy inDlv. 51.)

Bell System Technical J vol. 13, 1934, p. 461. (Copy in Div. 16.)

Date Mar. 15, 1938 Mar. 15, 1938 Oct. 15, 1940 Number 

